Theorems · Inductive type · algebraic geometry
AlgebraicGeometry.LocallyOfFiniteType
{X Y : AlgebraicGeometry.Scheme} → (X ⟶ Y) → PropA morphism of schemes f : X ⟶ Y is locally of finite type if for each affine U ⊆ Y and
V ⊆ f ⁻¹' U, The induced map Γ(Y, U) ⟶ Γ(X, V) is of finite type.
- Cited by
- 59 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- AlgebraicGeometry.Schemestatement · cited by 2,540
Cited by71
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.residueFieldIsoBasestatement and proof · cited by 6
- AlgebraicGeometry.Scheme.Hom.quasiFiniteLocusstatement and proof · cited by 6
- AlgebraicGeometry.Scheme.Hom.finiteType_appLEstatement · cited by 6
- AlgebraicGeometry.pointOfClosedPointstatement and proof · cited by 6
- AlgebraicGeometry.pointEquivClosedPointstatement and proof · cited by 4
- AlgebraicGeometry.Scheme.PartialMap.ofFromSpecStalkstatement and proof · cited by 3
- AlgebraicGeometry.spread_out_of_isGermInjective'statement and proof · cited by 3
- AlgebraicGeometry.LocallyOfFiniteType.isLocallyNoetherianstatement and proof · cited by 2
- AlgebraicGeometry.LocallyOfFiniteType.jacobsonSpacestatement and proof · cited by 2
- AlgebraicGeometry.LocallyQuasiFinite.of_finite_preimage_singletonstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_iff_isOpen_singleton_asFiberstatement and proof · cited by 2
- AlgebraicGeometry.isProper_eqstatement and proof · cited by 2